A letter is chosen at random from the letters of the word 'PROBABILITY'. Find the probability that the letter chosen is a
vowel.

Answer

To find the probability that a letter chosen at random from the word 'PROBABILITY' is a vowel, we can follow these steps:

### Step 1: Identify the total number of letters in the word 'PROBABILITY'.
The word 'PROBABILITY' consists of the following letters: P, R, O, B, A, B, I, L, I, T, Y.

**Total number of letters = 11.**

### Step 2: Identify the vowels in the word.
The vowels in the English language are A, E, I, O, U. In the word 'PROBABILITY', the vowels present are:
- A
- I
- O
- I

**Counting the vowels:**
- A: 1
- I: 2
- O: 1

**Total number of vowels = 4.**

### Step 3: Calculate the probability of choosing a vowel.
The probability of an event is calculated using the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case:
- Number of favorable outcomes (vowels) = 4
- Total number of outcomes (letters) = 11

So, the probability \( P \) of choosing a vowel is:

\[ P(\text{vowel}) = \frac{4}{11} \]

### Final Answer:
The probability that the letter chosen is a vowel is \( \frac{4}{11} \).

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